Abstract: Modular structure is pervasive in many complex networks of interactionsobserved in natural, social and technological sciences. Its study sheds lighton the relation between the structure and function of complex systems.Generally speaking, modules are islands of highly connected nodes separated bya relatively small number of links. Every module can have contributions oflinks from any node in the network. The challenge is to disentangle thesecontributions to understand how the modular structure is built. The mainproblem is that the analysis of a certain partition into modules involves, inprinciple, as many data as number of modules times number of nodes. To confrontthis challenge, here we first define the contribution matrix, the mathematicalobject containing all the information about the partition of interest, andafter, we use a Truncated Singular Value Decomposition to extract the bestrepresentation of this matrix in a plane. The analysis of this projection allowus to scrutinize the skeleton of the modular structure, revealing the structureof individual modules and their interrelations.